Currently, the resonators of HBAR type derive from the uses of high order harmonics, which can range from 10 to 100 times the fundamental frequency of said resonator, in bulk wave resonators such as the quartz resonators for example. Their initial application was to make it possible to limit the decrease in the electromechanical coupling factor of a composite resonator made up of a piezoelectric layer, its electrodes, and an additional layer providing for a mechanical support, a temperature compensation, or even simply the fabrication of the resonator.
When the substrate becomes very thick relative to the piezoelectric layer, the resonator becomes an HBAR or OMR (Overmoded Resonator) resonator rather than a composite resonator. These resonators have applications in fields where high quality factors are needed. In practice, resonators consisting of a thin film on a bulk substrate of a material exhibiting low propagation losses, such as quartz as described in the paper by H. Zhang, W. Pang, H. Yu and E. S. Kim, entitled High-tone bulk acoustic resonators on sapphire, crystal quartz, fused silica and silicon substrates, J. Appl. Phys. Vol. 99, 124911 (2006), YIG (Ytrium Ion Garnet), lithium tantalate as described in the paper by H. L. Salvo, M. Gottlieb and B. R. McAvoy, entitled Shear mode transducers for high-Q bulk microwave resonators, in Proceedings of the 41st Annual Frequency Control Symposium, p. 388-390 (1982), lithium niobate as described in the paper by D. Gachon, E. Courjon, J. Masson, V. Petrini, J. Y. Rauch, S. Ballandras, entitled LiNbO3-LiNbO3 high overtone bulk acoustic resonator exhibiting high Q.f product, in Proceedings of the 2007 IEEE Ultrasonics Symposium, p. 1417-1420, corindon as described in the paper by K. M. Lakin, G. R. Kline and K. T. McCarron, entitled High-Q microwave acoustic resonators and filters, IEEE Transactions on Microwave Theory and Techniques, vol. 41 No. 2, p. 2139-2146 (1993) or sapphire as described in the paper by G. R. Kline, K. M. Lakin and K. T. McCarron, Overmoded high-Q resonators for microwave oscillators, in Proceedings of the 1993 IEEE International Frequency Control Symposium, p. 718, make it possible to obtain very high quality factors at relatively high frequencies (up to more than 30 000 at 2 GHz).
In this configuration, illustrated in FIG. 1, the thin piezoelectric film Piezo, inserted between a top electrode Es and a bottom electrode Ei, acts as both an excitation and reception transducer, while the properties of propagation of the acoustic wave Oac in the substrate S are exploited. To obtain high quality factors, it is therefore necessary to employ harmonics of a high order in order for the transducer to occupy only a small portion of the complete resonator and thereby be only little involved in the length of propagation of the wave.
This type of resonator offers the advantage of using substrates made of material with low losses and therefore high quality factor.
The drawback however is that the frequency spectrum of such a resonator consists of a series of evenly spaced resonances, the difference in frequency between these resonances corresponding to the fundamental resonance frequency of the component, as a first approximation primarily defined by the thickness of the substrate and the speed of propagation of the waves therein. Such a spectrum is represented in FIG. 2 for the case of an AlN/silicon resonator which provides the electrical response of an HBAR resonator, in terms of normalized conductance as a function of frequency.
The multitude of resonances, spaced apart by a few MHz only for substrates of the order of 500 μm to 1 mm in thickness, is problematic for time standard applications, because the oscillator circuits can indiscriminately be set to oscillate on one or the other of the resonances and thus produce an a priori random frequency. Jumps from one frequency to the other can even occur in the case of very significant instabilities.
To overcome these problems, a number of solutions have been proposed in the literature.
A first method consists in increasing the spacing between the resonances of the HBAR. This difference is defined as a first approximation by the relationship:
      Δ    ⁢                  ⁢    f    ≈      V          2      ⁢                          ⁢      e      in which V is the speed of the acoustic wave exploited in the substrate and e is the thickness thereof. Since the speed of propagation is an intrinsic characteristic of the material, the only way to increase the frequency difference Δf is to reduce the thickness of the substrate. As an example, FIG. 3 presents the theoretical effect of the thinning of the substrate of an AlN/sapphire resonator from 400 to 25 μm.
In this case, the periodicity of the resonances changes from 14 to 224 MHz. With such a frequency difference, the risks of frequency jumps from one resonance to the other are greatly limited, all the more so as the elements of the oscillation circuit generally have a limited bandwidth and therefore a tendency to attenuate the unused resonances. Another advantage of this method is that it makes it possible, as shown by the curves of FIGS. 3a and 3b which illustrate the trend of the conductance and of the susceptance as a function of the frequency respectively in the cases of HBAR resonators of AlN with a thick substrate (400 μm) and a thin sapphire substrate (25 μm), to increase the amplitude of the resonance peaks, and therefore better define them, because of an increase in the electromechanical coupling factor of the different resonances. This factor, which represents the capacity of the component to convert electrical energy into mechanical energy, and vice-versa, is in fact greatly limited by the presence of a thick substrate, which contributes only to the storage of mechanical energy, but not to its restoration in electrical form.
Despite these advantages, this solution does, however, suffer from two major drawbacks:                by reducing the thickness of the substrate, the proportion taken by the volume of the transducer and of the electrodes, and therefore the contribution of the layers having relatively low mechanical quality factors, are increased: for great thickness reductions, a significant degradation of the quality factor of the resonances is noted;        moreover, although thinning solutions do exist for materials like silicon or quartz, they are difficult to implement for materials such as lithium niobate where problems of parallel alignment between the eroded face and the native face arise (as described in the paper by M. Pijolat, S. Loubriat, S. Queste, D. Mercier, A. Reinhardt, E. Defaÿ, C. Deguet, L. Clavelier, H. Moriceau, M. Aïd and S. Ballandras, entitled Large electromechanical coupling factor film bulk acoustic resonator with X-cut LiNbO3 layer transfer, Appl. Phys. Lett. 95, 182106 (2009)), but also problems of generation of crystalline defects in the thinned materials. These two effects both contribute to an even greater degradation of the quality factor of the component. Moreover, for some materials such as sapphire or diamond, the thinning methods are virtually non-existent.        
The other approaches described in the literature propose circumventing these problems by adding a filtering structure to the resonators. For example, authors have proposed producing bulk wave bandpass filters co-integrated with HBAR resonators as described in the paper by W. Pang, H. Zhang, J. J. Kim, H. Yu and E. S. Kim, entitled High-Q single mode high-tone bulk acoustic resonator integrated with surface-micromachined FBAR filter, Proceedings of the 2005 MTT-S International Microwave Symposium, p. 413. These filters are produced from resonators obtained by the same technological steps of electrode and piezoelectric layer deposition, but on top of a locally positioned sacrificed layer that is removed at the end of fabrication to leave the resonators that make up the filter acoustically isolated from the substrate by a blade of air, as shown in FIG. 4. The bandpass filter selects only one or more resonances and greatly attenuates the others. However, in practice, the quality factors obtained have proven to be relatively low (3600 at 2.5 GHz), because of the additional electrical losses brought about by the presence of the filter as described in the paper by W. Pang, H. Zhang, J. J. Kim, H. Yu and E. S. Kim, entitled High-Q single mode high-tone bulk acoustic resonator integrated with surface-micromachined FBAR filter, Proceedings of the 2005 MTT-S International Microwave Symposium, p. 413.